Source: https://guthlabs.ai/docs/instruments/slope-stability-infinite-slope-method/
instrument / verified-clean
# Slope Stability — Infinite Slope Method
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration
**Tranche**: tranche-5
**Evidence ID**: t5-147
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The stated formula is a valid simplified infinite-slope factor-of-safety equation under the listed assumptions. The specification cannot receive PASS until gamma_w, the exact definitions of z and m, and the effective-stress meaning of c and phi are made explicit. The honest label is directionally correct but should also state the homogeneous-soil, planar-failure, steady-groundwater, and effective-stress assumptions.
### Formula and scope findings
- The formula is standard only when z is the vertical depth above the failure plane and m is the ratio of saturated vertical depth to total vertical depth, with 0 <= m <= 1; neither definition is specified.
- The formula uses gamma_w, but gamma_w is missing from the declared inputs. The specification must state that gamma_w is fixed at approximately 9.81 kN/m^3 or add it as an input.
- c and phi must be effective-stress parameters c' and phi' for the pore-pressure correction to be physically consistent; this is not stated.
### Unit assumptions
- beta and phi are angles in degrees in the user interface and must be converted to radians before JavaScript trigonometric functions are called.
- c and gamma*z must use consistent stress units, such as c in kPa and gamma in kN/m^3 with z in m.
- gamma and gamma_w must use the same unit system, such as kN/m^3.
- z is assumed to be vertical soil depth, not depth measured normal to the slope.
- m is assumed dimensionless and represents the saturated vertical-depth ratio above the failure plane.
- The standard water unit weight gamma_w = 9.81 kN/m^3 is used in the numerical examples.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
The formula is undefined at phi=90° because tan(phi) requires division by cos(phi)=0; an implementation that returns a numeric FS instead of rejecting the input is broken. A second hazard is the undocumented interpretation of signed beta, which can produce a misleading negative factor of safety.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"beta_deg": 45,
"phi_deg": 45,
"c_kPa": 10,
"gamma_kN_per_m3": 18,
"gamma_w_kN_per_m3": 9.81,
"z_m": 2,
"m": 0.5
},
"expected_outputs": {
"FS": 1.28305556
},
"working": "Convert angles: beta = 45 degrees, phi = 45 degrees; sin(beta) = 0.70710678, cos(beta) = 0.70710678, cos^2(beta) = 0.5, tan(phi) = 1. Effective unit weight term = gamma - gamma_w*m = 18 - 9.81*0.5 = 13.095 kN/m^3. Numerator = c + (gamma - gamma_w*m)*z*cos^2(beta)*tan(phi) = 10 + 13.095*2*0.5*1 = 23.095 kPa. Denominator = gamma*z*sin(beta)*cos(beta) = 18*2*0.70710678*0.70710678 = 18 kPa. FS = 23.095/18 = 1.28305556."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche5/tranche5-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`